What is -x^2+4x+3y^2-18y+8=0 ?

The solution to -x^2+4x+3y^2-18y+8=0 is Hyperbola with (h,k)=(2,3),a=sqrt(5),b=sqrt(15)

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-x^2+4x+3y^2-18y+8=0

- x^{2} + 4 x + 3 y^{2} - 18 y + 8 = 0

(h, k) = (2, 3), a = 5, b = 15

Solution steps

- x^{2} + 4 x + 3 y^{2} - 18 y + 8 = 0

Rewrite

- x^{2} + 4 x + 3 y^{2} - 18 y + 8 = 0

in the form of a standard hyperbola equation

\frac{( y - 3 ) ^{2}}{( 5 ) ^{2}} - \frac{( x - 2 ) ^{2}}{( 15 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 3), a = 5, b = 15

7 x^{2} - 9 y^{2} = 63

x^{2} - y^{2} - x + y - (- 10) = 0

y^{2} = (\frac{6}{5})^{2} + (2 - x)^{2}

\frac{- x ^{2}}{4} + \frac{y ^{2}}{4} = 1

y (y + 2) = x^{2}

What is -x^2+4x+3y^2-18y+8=0 ?
The solution to -x^2+4x+3y^2-18y+8=0 is Hyperbola with (h,k)=(2,3),a=sqrt(5),b=sqrt(15)